Factoring
x2 - 11x + 28
(x - 4)(x - 7)
g(x) = 3x – 7
a) find g(2)
b) find g(4y)
a) g(2) = -1
b) g(4y) = 12y - 7
Solve using substitution:
8x + 6y = 38 2y - 7x = -26
x = 4
y = 1
Add the following matrices:
[4 3 [7 8
9 -1] 2 12]
[11 11
11 11]
Simplify √252
6√7
x2 + 17x + 30
(x + 2)(x + 15)
1. f(x) = x2 – 3x + 7
a) find f(3)
b) find f(2k)
a) f(3) = 7
b) f(2k) = 4k2 - 6k + 7
Solve using elimination:
2y + 8x = 42 x - 5y = -42
x = 3
y = 9
Multiply the following matrices:
[4 9 [5 1
7 6] 8 2
1 3]
the number of columns in the first matrix do not match the number of rows in the second matrix ("inside" dimensions do not match), this can not be done.
Simplify
16-1/4
1/2
5g3w2 + 11g2w2 – 36gw2
gw2(5g - 9)(g + 4)
f(x) = 2x – 7 g(x) = x2 + 4 h(x) = 3x2 – 7x + 8
Find f o g (f composed of g)
f(g(x)) = 2x2 + 1
Solve using Cramer's Rule:
5x - 6y = 8 -2x+ 4y = 0
x = 4
y = 2
If you multiply a 3x4 matrix and a 5x3 matrix together, what will the dimensions of the product matrix be?
It can not be done, the number of columns in the first matrix do not match the number of rows in the second matrix.
(3 - 8i)2
48i - 55
5a2 + 23a – 42 = 0
a = 1.4
a = -6
f(x) = 2x – 7 g(x) = x2 + 4 h(x) = 3x2 – 7x + 8
Find g o f (g composed of f)
g(f(x)) = (2x - 7)2 + 4
4x2 - 28x + 53
Solve for f, g, and h.
3f - 2g = 12 4f = 32 4g - 6h + f = 20
f = 8
g = 6
h = 2
Find the inverse of this matrix:
[1 0 0
0 1 0
0 0 1]
[1 0 0
0 1 0
0 0 1]
When trying to solve an equation with a radical or complex number in the denominator, you must first _______.
rationalize the denominator
14a7x3y6 – 35a4x6y9 + 42a3x7y5
7a3x3y5(-5ax3y4 + 2a4y + 6x4)
f(x) = 2x – 7 g(x) = x2 + 4 h(x) = 3x2 – 7x + 8
Find h o g (h composed of g)
h(g(x)) = 3(x2 + 4)2 - 7x + 8
3x4 + 24x2 - 7x + 56
Solve for a, b, and c
a + 2b - 2c = 13 b + 2a + 4c = 16 3a - 4b + 7c = -8
a = 3
b = 6
c = 1
For a 2x2 matrix, the equation for ______ is |A|=ad-bc
determinant
8√y2 + 7√y - 4√y
8y + 3√y